TY  - JOUR
PY  - 2022//
TI  - A Cox model for gradually disappearing events
JO  - Probability in the engineering and informational sciences
A1  - Jang, Jiwook
A1  - Qu, Yan
A1  - Zhao, Hongbiao
A1  - Dassios, Angelos
SP  - ePub
EP  - ePub
VL  - ePub
IS  - ePub
N2  - Innovations in medicine provide us longer and healthier life, leading lower mortality. Sooner rather than later, much greater longevity would be possible for us due to artificial intelligence advances in health care. Similarly, Advanced Driver Assistance Systems (ADAS) in highly automated vehicles may reduce or even eventually eliminate accidents by perceiving dangerous situations, which would minimize the number of accidents and lead to fewer loss claims for insurance companies. To model the survivor function capturing greater longevity as well as the number of claims reflecting less accidents in the long run, in this paper, we study a Cox process whose intensity process is piecewise-constant and decreasing. We derive its ultimate distributional properties, such as the Laplace transform of intensity integral process, the probability generating function of point process, their associated moments and cumulants, and the probability of no more claims for a given time point. In general, this simple model may be applicable in many other areas for modeling the evolution of gradually disappearing events, such as corporate defaults, dividend payments, trade arrivals, employment of a certain job type (e.g., typists) in the labor market, and release of particles. In particular, we discuss some potential applications to insurance.<p />  <p>Language: en</p>
LA  - en
SN  - 0269-9648
UR  - http://dx.doi.org/10.1017/S0269964821000553
ID  - ref1
ER  -